We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics.
|Number of pages
|Journal of the Royal Statistical Society. Series B: Statistical Methodology
|Published - Sep 2010
Bibliographical noteKAUST Repository Item: Exported on 2020-04-23
Acknowledged KAUST grant number(s): KUSC1-016-04
Acknowledgements: We thank Maria-Pia Victoria-Feser for providing the Swiss consumption data. Ma's research was partially supported by National Science Foundation grant DMS-0906341. Genton's research was partially supported by National Science Foundation grants DMS-0504896 and CMG ATM-0620624, and award KUSC1-016-04 made by King Abdullah University of Science and Technology.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
- Complete statistic
- Estimation efficiency
- Latent variable
- Maximum likelihood estimator
- Quadrature points
- Score function
- Sufficient statistic
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty